Red Mites in Coop and Run - Treatment/Brand Suggestions??

This is our first infestation with mites, so I apologize if I sound ignorant, we have never done a full-out treatment before!

This past weekend we got several inches of rain, which briefly flooded the main run area and left the soil soggy for a day or two. Today, when I went out for the daily chicken care, I noticed red mites in the soil, especially around areas with chicken poop. They are also in the coop itself. There aren't a ton of them, but enough to the point where I feel it's time to treat the whole place. Our ladies seem perfectly fine and not in any discomfort, so the mites don't seem to have totally taken over yet (I assume if the mites get too bad the chickens start to feel uncomfortable or sickly).

Again this is our first time so I am in the dark about even where to begin researching brands. Anyone have any suggestions of brands that have worked well?? Since the mites are in the dirt as well I don't know if a special remover is needed?

We'd like to do a treatment on the coop this weekend to stop the mites as soon as we can, so a widely available brand is preferred so we can pick it up at our local feed store!

Are you positive they are chicken mites??
Don't think they would not be in the soil, but hiding in nice dry cracks and crevices inside the coop.
There area plethora of 'bugs' in the world, most will not bother your chickens.
Make sure they need to be poisoned before doing so.

Best done well after dark with a strong flashlight/headlight, easier to 'catch' bird and also to check for the mites that live in structure and only come out at night to feed off roosting birds.
Wipe a white paper towel along the underside of roost to look for red smears(smashed well fed mites).
Part the feathers right down to the skin around vent, head/neck and under wings.
Google images of lice/mites and their eggs before the inspection so you'll know what you're looking for.